24.241 | Fall 2009 | Undergraduate

# Logic I

Reading assignments are from the required textbook: Bergmann, Merrie, James Moor, and Jack Nelson. The Logic Book. 5th ed. New York, NY: McGraw-Hill, 2008. ISBN: 9780073535630.

1 Basic notions of logic; arguments; the connectives
2 Truth-functionality; introduction to sentential logic (SL) syntax and semantics; translation Chapter 1
3 Translation continued; problems with conditionals and other phenomena of natural language; truth-tables Chapter 2
4 Truth-tables and logical properties of compound sentences Chapter 3
5 Entailment and validity with truth-tables
6 Derivations in sentential logic (SD)
7 Derivations in SD/SD+ Chapter 5
8 Theorem-proving, review Chapter 6.1-6.2
9 Introduction to meta-theory; mathematical induction Chapter 6.3
10 Soundness of SD/SD+
11 Completeness of SD/SD+ Chapter 6.3-6.4
12 Introduction to predicate logic: Quantifiers, variables, constants, predicates, universe of discourse
13 Open sentences; free vs. bound variables; scope, multiply quantified sentences; definite descriptions; properties of relations
14 Identity; functions, translation to and from predicate logic (PL) Chapter 7.1-7.7
15 Translation to and from PL/PLE; “most”; donkey sentences
16 Informal PL/PLE semantics: Interpretations, substitutions, quantification truth, falsity, consistency, and equivalence, quantificational argument validity Chapter 7.8, 8.1-8.4
17 Formal PL/PLE semantics: Extensions, interpretations, variable assignments, satisfaction, truth and falsity under interpretations and variable assignments Chapter 7.9, 8.6
18 Formal PL/PLE semantics continued; review Chapter 8.7
19 Derivations in PD
20 Derivations in PD+/PDE Chapter 10.1-10.2
21 Derivations in PDE continued; preliminaries for meta-theory Chapter 10.4
22 Meta-theory: Soundness of PD, PD+, PDE
23 Meta-theory: Completeness of PD Chapter 11.3-11.4
24 Meta-theory: Completeness continued; PD+; PDE Chapter 11.1-11.4
25 Review

## Course Info

Fall 2009
##### Learning Resource Types
Problem Sets with Solutions
Exams
Lecture Notes